Question

Take nine numbers forming a square in a calendar and mark the four numbers at the corners.

Add the squares of diagonal pairs and find the difference of the sums.

3² + 19² = 370

17² + 5² = 314

370 – 314 = 56

(i) Do this for other such nine numbers.

(ii) Explain using algebra, why the difference is always 56. (it is convenient to take the number at the centre of the square as x – see the section

Answer 1

(ii) If we represent a square with 9 numbers

[(x – 8)² + (x + 8)²] – [(x + 6)² + (x – 6)²]

[x² + 8² + x² + 8²] – [x² + 6² + x² + 6²]

(8² + 8²) – (6² + 6²) = 128 – 72 = 56